The Theory of the Riemann Zeta-function


Author: Late Savilian Professor of Geometry E C Titchmarsh,Titchmarsh, Edward Charles Titchmarsh,Edward Charles Titchmarsh,D. R. Heath-Brown
Publisher: Oxford University Press
ISBN: 9780198533696
Category: Architecture
Page: 412
View: 1884

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The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

Exploring the Riemann Zeta Function

190 years from Riemann's Birth
Author: Hugh Montgomery,Ashkan Nikeghbali,Michael Th. Rassias
Publisher: Springer
ISBN: 3319599690
Category: Mathematics
Page: 298
View: 6323

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Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.

Schönheit und Geometrie der Zetafunktion

Beobachtungen und Skizzen
Author: Thomas Kromer
Publisher: BoD – Books on Demand
ISBN: 3842305389
Category: Mathematics
Page: 116
View: 8721

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Die Zeta- und die Etafunktion gehören zu den komplexesten Objekten der Mathematik. In einem strikt geometrischen Ansatz erhalten wir unerwartet schöne Bilder ihres Verlaufs durch die komplexe Zahlenebene, zum Teil verblüffende Zusammenhänge werden in 48 Farbabbildungen illustriert. So können wir nachvollziehen, warum Nullstellen nur für komplexe Zahlen s mit einem Realteil von 0,5 möglich sind. Die Riemannsche Vermutung wird plötzlich plausibel!

The Riemann Hypothesis

A Resource for the Afficionado and Virtuoso Alike
Author: Peter Borwein,Stephen Choi,Brendan Rooney,Andrea Weirathmueller
Publisher: Springer Science & Business Media
ISBN: 0387721258
Category: Mathematics
Page: 533
View: 1493

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The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

Mathematics for the General Reader


Author: E.C. Titchmarsh
Publisher: Courier Dover Publications
ISBN: 0486821188
Category: Mathematics
Page: 192
View: 7654

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"A first-class mathematician's lucid, unhurried account of the science of numbers from arithmetic through the calculus." — James R. Newman, The World of Mathematics. This highly accessible introduction to mathematics is geared toward readers seeking a firm grasp of the essentials of mathematical theory and practice. The treatment also offers a concise outline of mathematical history and a clearer notion of why mathematicians do what they do. Author E. C. Titchmarsh, who served for many years as Savilian Professor of Geometry at Oxford University, begins with counting and the fundamentals of arithmetic. He guides readers through the complexities of algebra, fractions, geometry, irrational numbers, logarithms, infinite series, complex numbers, quadratic equations, trigonometry, functions, and integral and differential calculus. Titchmarsh's graceful, fluid style helps make complicated topics easier to grasp, and his inclusion of numerous examples will prove especially helpful to readers with little or no background in mathematics.

Bulletin

Classe des sciences mathématiques et naturelles. Sciences mathématiques
Author: Srpska akademija nauka i umetnosti
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 951

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Functions of One Complex Variable I


Author: John B. Conway
Publisher: Springer Science & Business Media
ISBN: 9780387903286
Category: Mathematics
Page: 317
View: 7888

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This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

The Mysteries of the Real Prime


Author: M. J. Shai Haran
Publisher: Oxford University Press
ISBN: 9780198508687
Category: Mathematics
Page: 240
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Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.

CMFT


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Geometric function theory
Page: N.A
View: 7905

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Actas


Author: Antonio A. R. Monteiro
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6158

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Algebraische Zahlentheorie


Author: Jürgen Neukirch
Publisher: Springer-Verlag
ISBN: 3540376631
Category: Mathematics
Page: 595
View: 5741

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Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, modern und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie" vom "Arakelovschen Standpunkt", die bis hin zum "Grothendieck-Riemann-Roch-Theorem" führt.